For outcomes k in 0 to K, slope vector a, intercept vector c, and latent ability vector theta, the response probability function is
P(pick=0|a,c,th) = 1-P(pick=1|a,c_1,th)
P(pick=k|a,c,th) = 1/(1+exp(-(a th + c_k))) - 1/(1+exp(-(a th + c_(k+1))))
P(pick=K|a,c,th) = 1/(1+exp(-(a th + c_K)))
The number of choices available
the number of factors
whether to use a multidimensional model.
The graded response model was designed for a item with a series of
dependent parts where a higher score implies that easier parts of
the item were surmounted. If there is any chance your polytomous
item has independent parts then consider
If your categories cannot cross then the graded response model
provides a little more information than the nominal model.
Stronger a priori assumptions offer provide more power at the cost
an item model
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